SC 98-30 Peter Deuflhard, Martin Seebaß: Adaptive Multilevel FEM as Decisive Tools in the Clinical
Cancer Therapy Hyperthermia
Abstract: The paper surveys recent progress in a joint mathematical-medical
project
on cancer therapy planning. Within so-called regional hyperthermia
the computational task
is to tune a set of coupled radiofrequency antennas such that a carefully
measured tumor is locally heated, but any outside hot spots are
avoided.
A mathematical model of the whole clinical system - air, applicator with
antennas, water bolus, individual patient body - involves Maxwells
equations in
inhomogeneous media and a parabolic bioheat transfer equation, which
represents a
simplified model of heat transfer in the human body
(ignoring strong blood vessel heat transport). Both PDEs need to be computed
fast and to medical reliability (!) on a workstation within a clinical
environment. This requirement triggered a series of new algorithmic
developments to be reported here, among which is an adaptive multilevel
FEM for Maxwells equations, which dominates the numerical simulation time.
In total, however, the main bulk of computation time (see Table 3 in
Section 4 below) still goes into segmentation - a necessary
preprocessing step in the construction a 3D virtual patient from the
input of a stack of 2D computed tomograms (left out here).
Keywords: hyperthermia,
Maxwells equations,
nonlinear heat transfer,
finite elements
MSC: 65N30, 92C50